We introduce a systematic way of constructing 3D exotic massive gravity theories in the first order formulation.
Our method is based on truncating a single degree of freedom of the parity odd gravity models found in arXiv:1405.6213 and deforming their Lagrangian with appropriate potential terms such that the resulting models have a well-defined metric equation but their Bianchi identities are satisfied only on-shell. Hence, they are `third-way' consistent. We illustrate our approach by re-obtaining already
known exotic theories and then construct an extended exotic massive gravity model whose field equation is of order eight.
We also explain how to check Bianchi identities using the first order formulation.